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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Recursive functionals and quantifiers of finite types revisited. V

Author: S. C. Kleene
Journal: Trans. Amer. Math. Soc. 325 (1991), 593-630
MSC: Primary 03D65
MathSciNet review: 974519
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Abstract: This is the last in a sequence of papers that redoes the theory of recursion in finite types. A key feature of the theory is that a computation can succeed (or finish) even if some of its subcomputations do not, if these turn out to be irrelevant to the total computation. I give a detailed description of computations involving oracles for type $ 3$ functionals. The computation may be viewed formally as a transfinite sequence of symbolic expressions, but I also describe a semantics in which each expression is given a concrete realization.

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Article copyright: © Copyright 1991 American Mathematical Society